Multilayered plate elements for the analysis of multifield problems

Abstract

This work deals with advanced finite element (FE) formulations for the analysis of multilayered structures in the case of multifield problems. The following four fields are considered: mechanical, thermal, electrical and magnetic. Constitutive equations, in terms of coupled mechanical–thermal–electrical–magnetic field variables, are obtained on the basis of a thermodynamic approach. The four-field principle of virtual displacements is employed to derive FE matrices. Three-fields, two-fields as well as pure mechanical problems have been discussed as relevant particular cases. A condensed notation, known as Carrera unified formulation, has been employed to establish a comprehensive two-dimensional modeling with variable kinematic features. Layer-wise/equivalent single layers plate elements have been developed according to linear up to fourth-order expansion in the layer/plate thickness directions. FE matrices have been obtained in terms of a few fundamental nuclei whose dimension is 6×6 for the full four fields case. Numerical results show the effectiveness of the proposed implementation by encompassing various static and dynamic multifield plate problems.